Triangle ABC is split into two triangles as shown: shaded and non-shaded.
If the area of the shaded triangle is twice the area of the non-shaded triangle, find the size of angle ACB, correct to 1 decimal place.
Answers
Answer:
26.6°
Step-by-step explanation:
The area of a triangle is given by (1/2) * (base) * (height). The two triangles share the same height, so in order for the shaded triangle to have twice the area, its base must be twice that of the non-shaded triangle.
The non-shaded triangle is a right triangle with two 45° angles, so it's an isoceles right triangle with a base equal to its height.
This means that the height of the shaded triangle is 1/2 of its base. Knowing that we can get the angle of ACB with:
tan⁻¹(1/2) ≈ 0.4636476 (in radians)
Convert to decimal angle:
0.4636476 * (180/π) ≈ 26.6°
Related Questions
si entre 2 obreros tardan 10 días en hacer una carretera, ¿cuánto tardarán en hacer el mismo trabajo 4 obreros?
Answers
Answer:
5 dias
Step-by-step explanation:
10/2= 5
Answer:
Tardarán:
5 días
Step-by-step explanation:
Se trata de una regla de tres:
2 obreros son a 10 días
4 obreros son a W días
W = 10*2/4
W = 5
PLEASE HELP ME ON THIS I NEED IT NOW
Answers
Answer:
Solution : (36, 42)
Step-by-step explanation:
It mention that the image is dilated by a scale factor of 6, and hence we will have to multiply each coordinate by 6 to receive the dilated point. Here we only want the dilation of point B,
B' = (6 [tex]*[/tex] 6, 7 [tex]*[/tex] 6) = (36, 42)
If quadrilateral ABCD is dilated by a scale factor of 6, then the coordinates of point B' are (36, 42).
( 3x + 8 ) - ( 2x + 7 ) when x=3
Answers
Answer:
4
Step-by-step explanation:
First, substitute x for 3 and simplify
(9 + 8) - (6 + 7)
Simplify again
17 - 13
Simplifly once more
4
answer 4
method: if x=3
Sol (3(3)+8) - (2(3)+7) changed x=3
Then multiply =(9+8) - (6+7)
Add and subtract = 17-13
Then subtract and you will have your answer =4
Hope it helped
Please mark brainliest :)
You buy six T-bone steaks that cost $15.99 per pound. The weight that is listed on the package is 5.77 pounds. The scale that weighed the package is accurate to within 1 32 pound. How much per kilogram might you be undercharged or overcharged? (Round to the nearest cent.)
Answers
Answer:
$0.50
Step-by-step explanation:
Suppose that a person bought six T-bone steaks that cost $15.99 per pound
The weight that is listed on the package is 5.77 pounds.
The scale that weighed the package is accurate to within 1/32 pound
Let assume x is the range of the weight listed on the package,
Then:
[tex]|x-5.77| \leq \dfrac{1}{32} \ --- \ (1)[/tex]
Using the method of absolute value inequality;
[tex]- \dfrac{1}{32} \leq x -5.77 \leq \dfrac{1}{32}[/tex]
[tex]5.77- \dfrac{1}{32} \leq x \leq \dfrac{1}{32}+ 5.77[/tex]
[tex]5.77- 0.03125\leq x \leq 0.03125+ 5.77[/tex]
[tex]5.73875 \leq x \leq 5.80125[/tex]
The amount per kilogram undercharged or overcharged is :
[tex]=\dfrac{1}{32} \times 15.99[/tex]
= $0.50
120 men had provisions for 200 days. After 5 days, 30 men died due to an epidemic. The remaining food will last for _______________ Proportion (a) 146 1/4 days (b) 150 days (c) 2251/2 days (d) 260 days
Answers
Answer:
the answer is 150 days
Step-by-step explanation:
that is the answer
I need help ASAP
Integrated math ll
Answers
Answer:
x = 15 and y = 30
Step-by-step explanation:
We see that 4x + 15 + 5x + 30 = 180.
We can solve for x:
9x + 45 = 180
9x = 135
x = 15.
We also see that 5x + 30 is equal to 3y + 15, so we can solve for y:
5x + 30 = 3y + 15
5 (15) + 30 = 3y + 15
3y = 75 + 30 - 15
3y = 90
y = 30.
After an exercise, Ali and Ben measured their heart rates. The ratio of their heart rates was 15:17 Bens heart beats 18 times per minute more than Ali. Calculate Ali heart rate
Answers
Answer:
Ali's heart rate is 135 times per minute.
Step-by-step explanation:
Let Ali's heart rate be denoted by x times per minute.
It is provided that Ben's heart beats 18 times per minute more than Ali.
The ratio of their heart rates was 15:17.
That is:
[tex]\frac{15}{17}=\frac{x}{x+18}[/tex]
Solve for x as follows:
[tex]\frac{15}{17}=\frac{x}{x+18}[/tex]
[tex]15(x+18)=17x\\15x+270=17x\\2x=270\\x=135[/tex]
Thus, Ali's heart rate is 135 times per minute.
Question of the day
Jack had lunch with two friends. Their bill for lunch was $29.46.
They want to add a tip of $5.25 and divide the total equally. How
much should each person pay?
.pdf
O $4.57
O $9.82
O $11.57
O 17.36
Answers
Answer:
$11.57
Step-by-step explanation:
First, find the total amount they need to pay.
Add the bill for lunch and the tip amount.
bill + tip
The bill was $29.46 and the tip was $5.25
$29.46 + $5.25
$34.71
The total amount with tip is $34.71
Next, find the amount each person should pay.
They want to divide the amount equally. There are 3 total people ( Jack + 2 friends = 3 people). Divide the total ($34.71) by 3.
$34.71 /3
$11.57
Each person should pay $11.57
The measure of an angle is 8 degrees less than three times the measure of the angle's supplement. Find the measure of the angle.
Answers
Answer:
262
Step-by-step explanation:
3(90) - 8 = x
270-8 = x
262 = x
36__3__12__6__1 = 36
Either add, subtract, multiply or divide these numbers to get 36 (use each symbol how ever many times as needed)
Answers
Answer:
36 * 3 - 12 * 6 * 1 = 36
Step-by-step explanation:
36 * 3 - 12 * 6 * 1 = 36
Shen sees this in a supermarket: 5 chickens for $18.25. What is the cost of one chicken
Answers
Answer:
$3.65 per chicken
Step-by-step explanation:
Divide the coat of he chickens by the number of chickens.
18.25/5
= 3.65
So one chicken would cost $3.65.
Answer:
$3.65
Step-by-step explanation:
$18.65/5=$3.65
1 chicken=$3.65
Find the value of a.
b
83°
520
Answers
Multiply.
(3 – 4i)(–2 – 2i)
Enter your answer in the box.
Answers
Answer:
[tex]\Huge \boxed{-14 + 2i}[/tex]
Step-by-step explanation:
(3 – 4i)(–2 – 2i)
Expanding brackets.
3(-2 - 2i) - 4i(-2 - 2i)
-6 -6i + 8i + 8i²
Apply imaginary number rule : i² = -1
-6 - 6i + 8i + 8(-1)
-6 - 6i + 8i - 8
Combining like terms.
-6 - 8 - 6i + 8i
-14 + 2i
Which expression is equivalent to StartRoot StartFraction 8 Over x Superscript 6 Baseline EndFraction EndRoot? Assume x Greater-than 0. StartFraction x cubed StartRoot 2 EndRoot Over 2 EndFraction StartFraction 4 StartRoot 2 EndRoot Over x cubed EndFraction StartFraction StartRoot 2 EndRoot Over 2 x cubed EndFraction StartFraction 2 StartRoot 2 EndRoot Over x cubed EndFraction
Answers
Answer:
D
Step-by-step explanation:
The expression is equivalent to [tex]\rm \frac{2 \sqrt2}{x^3}[/tex]. Option D is correct.
What is the definition of a fraction number?
A fraction number is a number that represents a portion of a larger number, where the larger number might be any integer. It has the shape of a numerator and a denominator.
The given expression is;
[tex]\rm \sqrt {\frac{8}{x^6}}[/tex] x>0
The square root of 8 is 2√2 and x⁶ is x³.
The expression is equivalent to [tex]\rm \frac{2 \sqrt2}{x^3}[/tex].
Hence, option D is correct.
To learn more about fraction numbers, refer to https://brainly.com/question/8602593
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Write an equation of each line in standard form with integer coefficients. y=4.2x+1.8
Answers
Answer: -21x + 5y = 9
Step-by-step explanation:
The standard form says that Ax + By=C
So to covert y = 4.2x + 1.8 into subtract 4.2 from both sides.
y = 4.2x + 1.8
-4.2x -4.2x
-4.2x + 1y = 1.8 Now it is written in standard form and to make the decimals integers we will multiply both sides by 10.
-4.2x(10) + 1y(10) = 1.8(10)
-42x + 10y = 18 which reduces to -21x + 5y = 9
in how many ways of the permutations of 10 different things taken 4 at a time will one particular thing always occur
Answers
Answer:
do as direct
which one of the following is square of 4
2
8
16
64
A 2-column table with 4 rows. Column 1 is labeled Store with entries A, B, C, D. Column 2 is labeled Unit price (per loaf) with entries 1 dollar and 98 cents, 1 dollar and 95 cents, 2 dollars and 1 cent, 2 dollars and 2 cents. From which store should Camillo buy bread to get the best price? Store A Store B Store C Store D
Answers
Answer:
B
Step-by-step explanation:
The lowest price in column 2 is $1.95 per loaf, at store B.
Answer: 48.75
Step-by-step explanation:
PLEASE HELP ME I'LL MAKE YOU BRAINLIEST!!!! In 1972, federal vehicle emission standards 3.4 grams hydrocarbons released per mile driven. By 2007, the standards allowed only 0.8 grams hydrocarbons per mile driven. What was the rate of change from 1972 to 2007? Please show work thank you
Answers
======================================================
Work Shown:
x = year
y = amount of hydrocarbon emissions in grams, per mile driven
m = rate of change = slope
m = (y2 - y1)/(x2 - x1)
m = (0.8 - 3.4)/(2007 - 1972)
m = -2.6/35
m = -0.0742857 approximately
The approximate rate of change is about -0.0742857 grams per year. The negative rate of change indicates the per mile hydrocarbon amount has gone down by about 0.0742857 grams each year.
Allen is showing his work in simplifying-8.3 + 9.2 - 4.4 + 3.7. Identify and explain any errors in his work or in his reasoning. Write feed back to Allen explaining the mistakes he made and how to correct his work
Answers
Answer:
Step-by-step explanation:
The question lacks Allen's workings. Find it below.
Step Work Reasoning
−8.3 + 9.2 − 4.4 + 3.7 Original problem
1 −8.3 + 9.2 + 4.4 + 3.7 Additive inverse
2 −8.3 + 4.4 + 9.2 + 3.7 Commutative property
3 −8.3 + (4.4 + 9.2 + 3.7) Associative property
4 −8.3 + 17.3 Simplify
5 9 Simplify
Given the equation −8.3 + 9.2 − 4.4 + 3.7, to solve this we are going to be using different properties.
Given three values A, B and C, the following are true:
A-B = A+(-B) Additive inverse
(A+B)+C = A+(B+C) Commutative property
Applying this laws to correct Allen's calculation
Original problem
−8.3 + 9.2 − 4.4 + 3.7
Applying the additive inverse property
−8.3 + 9.2 +(− 4.4) + 3.7 {since product of plus and minus sign still gives a minus sign)
Rearranging the equation based on signs according to the associative property we will have:
−8.3 +(-4.4) + 9.2 + 3.7
Using the commutative property to separate the positive variables from negative variables will give:
{−8.3 +(-4.4)} + {9.2 + 3.7}
Since {−8.3 +(-4.4)} + {9.2 + 3.7} = {9.2 + 3.7} + {−8.3 +(-4.4)}
Simplify the expressions in parenthesis:
= {−8.3 +(-4.4)} + {9.2 + 3.7}
= (-8.3-4.4)+(9.2+3.7)
= (-12.7)+(12.9)
= 0.2
From the above calculation, it can be seen that Allen made an error while using the additive inverse property in his first step. He should not have removed the minus sign. The negative sign was removed from step 1 which makes the remaining steps of his calculation to be wrong. Instead of replacing -4.4 directly with +4.4 he should have used the additive inverse property by replacing -4.4 with +(-4.4).
Answer:
but like can you tell us where he did it wrong
Jon borrows 5.50 from his friends to pay for snacks, and 12.75 from his sister to go the movies. How much does he need to repay
Answers
Answer:
18.25
Step-by-step explanation:
Add 5.50 and 12.75
5.50 + 12.75 = 18.25
Answer: 18.25
Step-by-step explanation:
Parallel lines p, q and r are cut by transversal t. Which of these describes how to find the value of x
1. Lines p and t are parallel, so the alternate exterior are congruent; x = 130
2. Lines q and r are parallel, so the interior angles are supplementary; x = 130
3. Lines p and r are parallel, so they alternate exterior angles are supplementary; x = 50
4. Lines q and r are parallel, so the corresponding angles are congruent; x = 50
Answers
Answer:
Lines p and t are parallel, so the alternate exterior are congruent; x = 130
Step-by-step explanation:
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The correct answer is 2. Lines q and r are parallel, so the interior angles are supplementary; x = 130
What is Transversal?A line that intersects more than two lines is known as transversal.A Transversal cuts the two parallel lines and the angles formed in the transversal are known as transversal angles.How many types of Transversal angles are there?
The types of transversal angles are as follows
Corresponding anglesAlternate Interior AnglesAlternate Exterior AnglesCo-interior AnglesWhy other options are incorrect?
Option 1. is incorrect because Lines p and t are not parallel
Option 3 is incorrect because alternate exterior angles is x= 130°
Option 4 is incorrect because x is not corresponding angle to 50°
Hence , Option 2 is correct and rest options are incorrect.
Learn more about transversal here
https://brainly.com/question/24607467
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(5^3)−4
pls help!!!!
Answers
Answer:
121
Step-by-step explanation:
5 Raise to the power of 3
125-4=
121
Answer:
Step-by-step explanation:
121 simplify the equation
A construction crew has just finished building a road. The crew worked for 10 days. If they built 314 kilometers of road each day, what is the total length of road they built?
Answers
Answer:
3140
Step-by-step explanation:
If they made 314 kilometers per day and they worked for 10 days, multiply:
[tex]314*10=3140[/tex]
The total length of the road is 3,140 kilometers.
Answer:
1st or each day=314km
Let x in km be the total km for 10 days
10=x
>314×10=x
X=3140km
Therefore, for 10days, the road constructed was 3140km
please help me on this i’ll mark u the brainliest
Answers
Hope this helps!
Answer:
Altitude
Step-by-step explanation:
A segment from a vertex of a triangle at right angles to the opposite side is an altitude.
Thus AB is an Altitude
I’m confused plz help meeee
Answers
If it's up then add then up , or you can trace it and move it up with paper.
Answer:
U'(-3, 1), M'(-1, 4), L'(-2, 0)
Step-by-step explanation:
To do a translation of 5 units up, add 5 to the y-coordinate of each point.
U(-3, -4) ----> U'(-3, -4 + 5) = U'(-3, 1)
M(-1, -1) ----> M'(-1, -1 + 5) = M'(-1, 4)
L(-2, -5) ----> L'(-2, -5 + 5) = L'(-2, 0)
Answer: The translated points are U'(-3, 1), M'(-1, 4), L'(-2, 0)
Guys help me pls I need it immediately
Answers
Answer:
Hey there!
First, we want to find the side length of the large triangle.
1/2bh=y cm^2
bh=2y cm^2
Since b and h are the same here, we have b^2= 2y, [tex]b=\sqrt{2y}[/tex].
And we have FC=[tex]\frac{\sqrt{2y} }{2}[/tex].
Area of shaded triangle: [tex]\frac{1}{2} (\frac{\sqrt{2y} }{2})(\frac{\sqrt{2y} }{2})[/tex].
This is equal to: [tex]\frac{1}{2}(\frac{2y}{4})[/tex], or y/4.
Let me know if this helps :)
There are 12 inches in 1 foot. And there are 3 feet in 1 yard. How many inches are there in 1 yard.
Answers
Answer:
36 inches
Step-by-step explanation:
1 yard = 3 feet = 3*12 inches = 36 inches
1 yard = 36 inches
Write and evaluate the expression. Then, select the correct answer.
two less than the quotient of a number and four, increased by ten;
evaluate when m = 12
Answers
Answer:
The answer is 11
Step-by-step explanation:
got `100%
PLEASE HELP ME REALLY QUICK
Answers
Answer:
41
Step-by-step explanation:
BDA = DBC+CBA
84=5x+3 + 6x-7
Combine like terms
84 = 11x-4
Add 4 to each side
84+4= 11x -4+4
88 =11x
Divide each side by 11
88/11 = 11x/11
8 = x
We want angle ABC
ABC = 6x-7
=6*8 -7
=48-7
=41
Answer:
∠ABC = 41°
∠ DBC = 43°
Step-by-step explanation:
6x-7 + 5x+3 = 84
6x + 5x = 84 - 3 + 7
11x = 88
x = 8
∠ABC = 6x-7
= 6*8 - 7
= 48 - 7
= 41°
∠ DBC = 5x + 3
= 5*8 + 3
= 40 + 3
= 43°
what is 1/3 to the power of 2
Answers
Answer:
Brainliest!
Step-by-step explanation:
1/3 is going to be like
1^2
------
3^2
= 1/9